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Specifying Domain and Range Domain and Range Describing the domain and range of a function is a common task and an important part of mathematical vocabulary. As you study various functions and examine various graphs and their symbolic representations you will be expected to give the domain and range. In this lesson you will practice several ways of stating a domain or range. In this graph the x values are from 2 to 8. The open circle at 8 indicates that this point is not included in the domain. The y values, or range, consist of the values between 1.5 and 6. Note that 1.5 is included in the range, but 6 is not. See how these values are indicated using each of the three methods in the chart below. Method Description Domain All real numbers between 2 and 8, including 2 Range All real number between 1.5 and 6, including 1.5 Inequality Signs 2 x 8 1.5 y 6 Interval Notation [2,8) [ 1.5, 6 ) Example 1 Infinity The infinity symbol “ ” is helpful when the domain or range continues forever in the positive direction. Method Domain Description All real numbers greater than -4 Range All real number greater than -5 Inequality Signs 4 x 5 y Interval Notation (-4 , ) (-5 , ) Example 2 Double Infinity Method Description Domain All real numbers Range All real numbers equal to or greater than –3 and less than or equal to 1 Inequality Signs -x 3 y 1 Interval Notation (- , ) [-3 , ] Practice Exercises For each relation state the domain and range using appropriate notation, and indicate whether the graph is a function. 1. 2. 3. Domain: Range: Function: Domain: Range: Function: Domain: Range: Function: 4. 5. 6. Domain: Range: Function: Domain: Range: Function: Domain: Range: Function: 7. 8. 9. Domain: Range: Function: Domain: Range: Function: Domain: Range: Function: 10. 11 12. Domain: Range: Domain: Range: Domain: Range: Function: Function: Function: